Bus from Ciudad de La Habana (Estación Central de Ómnibus) to Batabanó (Habana province, south of the capital): 5 CUP for everybody (Astro bus). Go to the small ticket office of the NCC company (hard to find, better ask where it is) in the Estación Central de Ómnibus. You get a reservation for Batabanó (if you pay in CUC, you'll have reserved places so you this reservation is a guarantee to leave) plus a ticket for a right to go on the bus (you pay inside). I'm not sure about the bus leaving hours, but they seem to be in the morning (09:00-12:00?).

The boat ("Kometa" catamaran) costs 50 pesos per person (25 for children of less than 12 years of age):

50 CUC for foreigners

50 CUP for locals.

No reservations needed to go to the island. Best to buy a ticket with one day in advance for the return (or you'll have to wake up at 05:00 to leave at 12:00). 1 to 2 boats daily, excepts on Sundays.
The trip isn't an experience per se (modern, long, highly cooled air, can't go on deck....)

No bicycle can be brought on the island. Knives and the such must be checked in (free, secure and minimal loss of time).

Nice beach near Nueva Gerona. Poorly managed as of 2006-12 (rotting algae on the beach) but nice sea. There's a key about 1 km away from the beach (Cayo de los Monos) that can be accessed through vigorous swimming. It's also a nice place for sportive diving.

Nice 20 min hike to the hills that oversee Nueva Gerona. Physical but nice. Ask for directions to get to the base of a hill (near "la Cueva del Agua") then just go up following trails when you find them. The base of the hill is filled with rubbish heaps but the top and the middle are nearly pristine.